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" A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same... "
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Página 1
por Euclides - 1853
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The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science

1874 - 500 páginas
...a definition is to be attempted at all, it would be hard to produce a better than the old one — " A straight line is that which lies evenly between its extreme points ;" but, of course, the word evenly as much requires definition as the word straight. Mr. Wilson adds...
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Popular Science Monthly, Volumen68

1906 - 600 páginas
...has no magnitude. 2. A line is length without breadth. 3. The extremities of a line are points. 4. A straight line is that which lies evenly between its extreme points. 6. A superficies is that which has only length and breadth. 7. A plane superficies is that in which,...
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Philosophical Magazine

1874 - 550 páginas
...a definition is to be attempted at all, it would be hard to produce a better than the old one — " A straight line is that which lies evenly between its extreme points ;" but, of course, the word evenly as much requires definition as the word straiyht. Mr. Wilson adds...
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Matters Mathematical

I. N. Herstein, Irving Kaplansky - 1978 - 256 páginas
...has no magnitude. 2. A line is length without breadth. 3. The extremities of a line are points. 4. A straight line is that which lies evenly between its extreme points. Styles of mathematical exposition have changed. These are highly descriptive phrases, somewhat in the...
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The how and the why: An Essay on the Origins and Development of Physical Theory

David Park - 1990 - 488 páginas
...begins his Elements with a group of definitions, such as "a point is that which has no parts," and "a straight line is that which lies evenly between its extreme points." Let us not worry about whether these words uniqurly define what they are supposed to define; we know...
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George Boole: Selected Manuscripts on Logic and its Philosophy

Ivor Grattan-Guinness, Gerard Bornet - 1997 - 310 páginas
...defined and needing directly or indirectly a supplementary addition. Of this kind is the definition A straight line is that which lies evenly between its extreme points.* The idea conveyed is that of similarity and uniformity not only of the different parts of the line...
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Mathematically Speaking: A Dictionary of Quotations

C.C. Gaither, Alma E Cavazos-Gaither - 1998 - 484 páginas
...treatises on that subject. A point is defined to be that "which has no parts and which has no magnitude"; a straight line is that which "lies evenly between its extreme points." ... In this case the explanation is a great deal harder than the term to be explained, which must always...
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Geometry: Ancient and Modern

John R. Silvester - 2001 - 332 páginas
...which has no magnitude. Il. A line is length without breadth. III. The extremities of a line are poims, IV. A straight line is that which lies evenly between its extreme poims, The tendency nowadays, when first confromed by this, is to start to poke fun. What are these...
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Einstein's Legacy: The Unity of Space and Time

Julian Seymour Schwinger - 2002 - 274 páginas
...points, straight lines, circles, ellipses, and triangles. From Book l of the Elements: Definition 4, 1. A straight line is that which lies evenly between its extreme points. lt is quoted, not for its clarity, but its spirit. We would say that a straight line is the shortest...
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Reforming Philosophy: A Victorian Debate on Science and Society

Laura J. Snyder - 2010 - 386 páginas
...(within Euclidean geometry) only because of how Euclidean geometry defines "straight line" (that is, "A straight line is that which lies evenly between its extreme points"). The axiom would not even be true, let alone necessary, if our geometry defined "straight line" as one...
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